The Quadruple Bonding in C 2 Reproduces the Properties of the Molecule Sason Shaik, David Danovich, Benoît Braïda, Philippe C. Hiberty To cite this version: Sason Shaik, David Danovich, Benoît Braïda, Philippe C. Hiberty. The Quadruple Bonding in C 2 Reproduces the Properties of the Molecule. Chemistry - A European Journal, Wiley-VCH Verlag, 2016, 22 (12), pp.4116–4128. 10.1002/chem.201600011. hal-01627878 HAL Id: hal-01627878 https://hal.archives-ouvertes.fr/hal-01627878 Submitted on 10 Nov 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. The Quadruple Bonding in C2 Reproduces the Properties of the Molecule Sason Shaik,*[a] David Danovich,[a] Benoit Braida,[b] and Philippe C. Hiberty*[c] The paper is dedicated to Andreas Savin, a great scientist and a Mensch, on occasion of his 65th birthday Abstract: Ever since Lewis depicted the triple bond for acet- strength of which is estimated as 17–21 kcalmolÀ1. Alterna- ylene, triple bonding has been considered as the highest tive VB structures with double bonds; either two p bonds or limit of multiple bonding for main elements. Here we show one p bond and one s bond lie at 129.5 and 106.1 kcal À1 that C2 is bonded by a quadruple bond that can be distinctly mol , respectively, above the quadruply-bonded structure, characterized by valence-bond (VB) calculations. We demon- and they collapse to the latter structure given freedom to strate that the quadruply-bonded structure determines the improve their double bonding by dative s bonding. The use- key observables of the molecule, and accounts by itself for fulness of the quadruply-bonded model is underscored by 3 þ about 90% of the molecule’s bond dissociation energy, and “predicting” the properties of the Su state. C2’s very high re- for its bond lengths and its force constant. The quadruply- activity is rooted in its fourth weak bond. Thus, carbon and bonded structure is made of two strong p bonds, one first-row main elements are open to quadruple bonding! strong s bond and a weaker fourth s-type bond, the bond Introduction This fundamental question guided us ever since we started [6,7] the research on C2 and its isoelectronic species. Meanwhile, Ever since Cotton described the ReRe quadruple bonding in C2 is interesting also because of its chemistry and spectroscop- 2À [1] [8–10] Re2Cl8 , there has been a surge of interest in multiple bond- ic properties. Thus, C2 is no exotic curiosity, but an impor- ing,[2] reaching quintuple and even sextuple bonding in, for ex- tant chemical species.[11] It is responsible for the blue glow [3] [12] ample, Cr2,W2 and U2 complexes and dimers. In contrast to (“Swan bands”) emanating from hydrocarbon flames and for these high bond multiplicities among transition metals and cometic light.[8c,11] It is a constituent of solid-state carbides,[9] rare earths elements, we and our students with us have been and it is implicated in diamond growth[13] and in the formation [14] taught that the maximum bond multiplicity between two main of fullerenes. C2 is also one of the most strongly bound di- elements is a triple bond,[4] for example, as in acetylene, which atomic molecules in nature.[15] However, quite paradoxically, [4a] was asserted by Lewis to possess the highest possible union despite the strong bond in C2, this molecule is very highly re- between two atoms. Nevertheless, there are diatomic mole- active[8d,15] and is not isolable. Its reactivity may reflect the 3 [8d] cules, for example, C2, which possess eight valence electrons presence of the diradicaloid Pu state very close to the and a singlet ground state. Could it be that carbon breaks the ground state, or to simply originate from the multiply-bonded glass ceiling and has a quadruple bonding in this molecule?[5–7] nature of the ground state (or its inverted weak s bond; see later). Indeed, based on experience, the reactivity of multiply- bonded CC-based molecules increases with the bond multiplic- [a] Prof. S. Shaik, Dr. D. Danovich ity, so that triple bonds are frequently more reactive than [8e] Institute of Chemistry and double bonds, and both multiple bonds, in turn, are more The Lise Meitner-Minerva Center for Computational Quantum Chemistry reactive than single bonds. And for all these fundamental and Hebrew University of Jerusalem, 91904, Jerusalem (Israel) practical reasons, it is very important to reach a consensus E-mail: [email protected] about the nature of its bonding. Bonding is after all at the [b] Dr. B. Braida UPMC Universit Paris 06, CNRS UMR 7616 heart of chemistry. Laboratoire de Chimie Thorique A simplified molecular orbital (MO) consideration of bond C. 137, 4 Place Jussieu, 75252 Paris Cedex 05 (France) orders (BOs) suggests that C2 possesses a p double bond, as in [c] Dr. P. C. Hiberty 1 in Scheme 1. There is no underlying s bonding in 1, because Laboratoire de Chimie Physique, UMR CNRS 8000, Bat. 349 presumably the occupied bonding and anti-bonding orbitals, Universit de Paris Sud, 91405 Orsay Cdex (France) E-mail: [email protected] 2sg and 2su, cancel one another and contribute zero to the total BO. A related doubly-bonded picture was supported from energy decomposition analysis of a DFT calculation.[16a] Howev- the CC bonds. These observable properties indicate that the bond in C2 is somewhere between those in ethylene and ace- tylene.[20a,b,21] In addition, theoretical indices such as EBOs,[21] bond-strength orders (BSOs),[21b] and BOs based on localized natural orbitals[22] indicate bond orders of slightly more than two, reaching 2.5–2.6 (note however the BO(C2) in referen- ces [22b,c] is as large as that of HCCH and larger than in NN.[22d]). Furthermore, the domain-averaged Fermi holes [22b,c] (DAFH) analysis suggests that C2 has only a residual sigma bonding akin to Be2 (so-called “a non-classical sigma compo- nent”[22c]). Thus, these studies dismiss a “genuine quadruple [23] bond” in C2 and suggest a species like 1, with a p double bond and “a residual s interaction”, which Hermann and Fren- Scheme 1. Bonding cartoons: the p doubly-bonded model for C (1) sug- 2 [21a] gested by bond order consideration of the MO diagram, and the quadruply- king suggest to be two weak dative s bonds, as described [24] bonded model for C2 (2) suggested by qualitative VB consideration. The in- in 5 in Scheme 2. Alternatively, Weinhold and Landis pro- verted bond in [1.1.1] propellane (3), and the bonding cartoon of the triplet posed a similar type of s interaction, called “n bonding” (6), 3Sþ state (4)ofC. u 2 which they did not define as weak or residual bonding (recall that BOs with NBO[17b] are close to 4). Thus, all the recent criti- [20a,b,21,22] cisms of the quadruple bonding idea in C2 agree on [21a,b] er, usage of standard DFT may be questioned, since C2 has a “double-bond-plus” model, and their major criticism is a multireference character.[16b] Similarly, usage of a full-valence that the proposed quadruple bonding model is, allegedly, dis- CASSCF and wave function or other correlated methods leads connected from any observable of the C2 molecule. to effective BO (EBO) values of 2.2–3.0.[6] Other BO (e.g., or Wi- berg’s WBI, NBO-based BO) or EBO determination methods reveal values of 3.30, 3.40, 3.51, 3.71, and 3.9,[6,17] raising the doubt whether the naı¨ve BO/EBO calculations are reliable methods for determining the bond multiplicity of a molecule like C2, because of the fuzzy status of 2su. Indeed, as argued [6,15, 18] several times, the 2su orbital is weakly antibonding if not simply non-bonding, and hence counting this orbital in BO/ EBO considerations may distort the bonding picture (see later). An alternative starting point to the qualitative MO picture in Scheme 2. The dative bonding model (5), and the n-bonding model (6). 1 is 2 (Scheme 1), which can be deduced from qualitative va- lence bond (VB) considerations. Thus, sp-hybridization at each carbon atom leads to the straightforward model of C2 shown Therefore, in order to respond to this challenge, we focus in 2. Here, C2 possesses a quadruple bond made of an inner herein on the quadruply-bonded structure of C2 with an aim of triple bond (one s and two p bonds) and an outer fourth establishing that this structure by itself determines the key ob- s bond made from the inverted hybrids in 2. servable properties of the molecule, while other VB structures At first sight, the inverted hybrids in 2 might look rather have a marginal effect on these properties. Moreover, VB poorly matched for bonding. However, similarly inverted hy- theory does not interpret the wave function, as done by usage brids as in [1.1.1]propellane, 3 (Scheme 1), were shown to of EBO or other indices, but rather it directly gives a snapshot bring about significant bonding.[19] So why dismiss the inverted description of the bonds in terms of chemical Lewis structures.